Saudi Arabia is a kingdom in the Middle East with an area of 865,000 square miles, occupying about four-fifths of the Arabian Peninsula. With a population of about 10 million, this Muslim and Arab state is generally recognized as being formed in 1927 when Ibn Sa’ud united the country and was acknowledged as the sovereign independent ruler. Summer heat is intense in the interior, reaching 124°F, but it is dry and tolerable in contrast to coastal regions and some highlands, which have high humidity during the summer. Winters (December through February) are cool, with the coldest weather occurring at high altitudes and in the far north. A minimum temperature recorded at at-Turayf in 1950 was 10°F, and it was accompanied by several inches of snow and an inch of ice on ponds. Average winter temperatures are 74°F at Jidda and 58°F at Riyadh (the capital city), which has an annual precipitation of 2.5 to 3 inches.
After oil was discovered in Bahrain in 1932, many companies turned to Saudi Arabia and started exploring. Thus, in 1937, the American Arabian Oil Company, Inc. (AMARCO), was formed as a joint venture between Standard Oil Company of California (SOCAL) and the Government of Saudi Arabia to explore, produce, and market any petroleum found in the country. The year before, a geologist from SOCAL had discovered a small quantity of oil in the Eastern Province at Dammam Dome, on which the oil company town of Dhahran is now built. It was just beginning to be developed when another discovery was made—of what was to prove to be the largest oil field in the world. Called the Ghamar field, it would start Saudi Arabia on the road to becoming a highly developed country in just a generation. Located about 50 miles inland from the western shores of the Persian Gulf, the Ghamar field is a structural accumulation along 140 miles of a north–south anticline. The productive area covers approximately 900 square miles, and the vertical oil column is about 1,300 feet. It is generally considered to have recoverable reserves of about 75 billion barrels of oil. Total proven reserves in Saudi Arabia are estimated at more than 500 billion barrels, enough for more than a hundred years of production.
Since 1950, Saudi Arabia has experienced greater and more rapid changes than it had in the several preceding centuries. For example, during this time, as skilled nationals became available, more and more of the exploration, drilling, refining, and other production activities came under the control of the country. SOCAL was left primarily with the marketing and transportation functions outside the country.
During the 1960s, AMARCO increased its profitability substantially by hiring Dr. George Dantzig, then of the University of California, as a consultant. He supervised the development and implementation of LP models to optimize the production of different types of crude oils, their refining, and the marketing of some of their principal products. As a result of this effort, an operations research (OR) department was started in the company with the responsibility of continuing to review the firm’s operations to find other areas where costs might be decreased or profits increased by applications of OR.
Now attention is being focused on another aspect of one of the company’s small California refinery operations: the production of three types of aviation gasoline from the Saudi Arabian crude oil available. Recently, the marketing of petroleum products to the airline industry has become a rather substantial portion of AMARCO’s business. As shown in Figure 4.45, the three aviation gasolines, A, B, and C, are made by blending four feedstocks: Alkylate, Catalytic Cracked Gasoline, Straight Run Gasoline, and Isopentane.
In Table 4.14,TEL stands for tetraethyl lead, which is measured in units of milliliters per gallon (ml/gal). Thus, a TEL of 0.5 means there is 0.5 milliliter of tetraethyl lead per gallon of feedstock. Table 4.14 shows that TEL does influence the octane number but does not influence the Reid Vapor Pressure.
Each type of aviation gasoline has a maximum permissible Reid Vapor Pressure of 7. Aviation gasoline A has a TEL level of 0.5 ml/gal and has a minimum octane number of 80. The TEL level of aviation gasolines B and C is 4 ml/gal, but the former has a minimum octane number of 91, whereas the latter has a minimum of 100.
Assume that all feedstocks going into aviation gasoline A are leaded at a TEL level of 0.5 ml/gal and that those going into aviation gasolines B and C are leaded at a TEL level of 4 ml/gal. Table 4.15 gives the aviation gasoline data. A final condition is that marketing requires that the amount of aviation gas A produced be at least as great as the amount of aviation gas B.
Questions
1. AMARCO’s planners want to determine how the three grades of aviation gasoline should be blended from the available input streams so that the specifications are met and the income is maximized. Develop an LP spreadsheet model of the company’s problem.
2. Solve the linear programming model formulated in Question 1.
The following questions should be attempted only after Questions 1 and 2 have been answered correctly.
3. Suppose that a potential supply shortage of Saudi Arabian petroleum products exists in the near future due to possible damage to AMARCO’s oil production facilities from Iraqi attacks. This could cause the prices of the three types of aviation gasolines to double (while the values of the stocks remain the same, because they are currently on hand). How would this affect the refinery’s operations? If, after current stocks are exhausted, additional quantities must be obtained at values double those given in Table 4.14, how might AMARCO’s plans be affected?
4. Suppose that because of the new Iraqi crisis, the supply of alkylate is decreased by 1,800 bbl/day, catalytic cracked gas is decreased by 2,000 bbl/day, and straight run gasoline is decreased by 5,000 bbl/day. How does this affect AMARCO’s operations?
5. AMARCO is considering trying to fill the aviation gasoline shortage created by the new Iraqi crisis by increasing its own production. If additional quantities of alkylate, catalytic cracked gasoline, straight run gasoline, and isopentane are available, should they be processed? If so, how much of them should be processed, and how do their values affect the situation?
6. Due to the uncertainty about both the U.S. economy and the world economy resulting from the Iraqi crisis, AMARCO’s economists are considering doing a new market research study to reestimate the minimum requirement forecasts. With the economy continually weakening, it is felt that demand will decrease, possibly drastically, in the future. However, because such marketing research is expensive, management is wondering whether it would be worthwhile. That is, do changes in the minimum requirements have a significant effect on AMARCO’s operations? What is the change in profit from an increase or a decrease in the minimum requirements? Over what ranges of demand do these profit changes apply?
7. Suppose that the Middle East crisis ends and a flood of oil fills the marketplace, causing the prices of aviation gasoline to drop to $10.00, $11.00, and $11.50, respectively, for A, B, and C. How would this affect the company’s plans?
8. Suppose that the U.S. government is considering mandating the elimination of lead from aviation gasoline to decrease air pollution. This law would be based on new technology that allows jet engines to burn unleaded gasoline efficiently at any octane level. Thus, there would no longer be any need for constraints on octane level. How would such a new law affect AMARCO?
9. The Environmental Protection Agency is proposing regulations to decrease air pollution. It plans to improve the quality of aviation gasolines by decreasing the requirement on Reid Vapor Pressure from 7 to 6. Management is concerned about this regulation and wonders how it might affect AMARCO’s profitability. Analyze and make a recommendation.
10. The Marketing Department indicates that AMARCO will be able to increase its share of the market substantially with a new contract being negotiated with a new customer. The difficulty is that this contract will require that the amount of aviation gas A plus the amount of B must be at least as great as the amount of C produced. Because aviation gasolines A and B are least profitable of the three, this could cause a big decrease in profit for the company. However, marketing indicates that this is a short-run view, because the “large” increase in market share with the concomitant long-run profit increases will more than offset the “temporary small decrease” in profits because of the additional restriction.What do you recommend? Why?